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3 years ago

A line passes through the origin and the point (3,5). What is the slope of the line?

1 answer:

4 0

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 0}}\quad ,&{{ 0}})\quad 
% (c,d)
&({{ 3}}\quad ,&{{ 5}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{5-0}{3-0}$

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On a map, two inches equal 40 miles. If two cities are 115 miles apart, what is the distance between them on the map?

lora16 [44]

If 2 inches equals 40 miles, then 1 inch equals 20 miles.

115 miles/20 miles=5.75

The cities would be 5.75 miles apart on the map.

5 0

3 years ago

Express y = -2x² - 4x + 7 in the form of perfect square and find the maximum points.

Marat540 [252]

Answer:

<em>Maximum: (-1,9)</em>

Step-by-step explanation:

<u>Vertex form of the quadratic function</u>

If the graph of the quadratic function has a vertex at the point (h,k), then the function can be written as:

$y=a(x-h)^2+k$

Where a is the leading coefficient.

We are given the following function:

$y =-2x^2-4x+7$

To find the vertex, we need to complete squares. First, factor -2 on the first two terms:

$y =-2(x^2+2x)+7$

The expression in parentheses must be completed to represent the square of a binomial. Adding 1 and subtracting 1:

$y =-2(x^2+2x+1- 1)+7$

Taking out the -1:

$y =-2(x^2+2x+1)+2+7$

Factoring the trinomial and operating:

$y =-2(x+1)^2+9$

Comparing with the vertex form we have

Vertex (-1,9)

Leading coefficient: -2

Since the leading coefficient is negative, the function has a maximum value at its vertex, i.e.

Maximum: (-1,9)

3 0

2 years ago

Find the exact value. sin135°

Soloha48 [4]

Answer:

$\frac{1}{\sqrt{2} }$

Step-by-step explanation:

Note that

sin135° = sin(180 - 135)° = sin45° = $\frac{1}{\sqrt{2} }$ = $\frac{\sqrt{2} }{2}$

7 0

3 years ago

Which statement is true out of the value of money that you save increases over time , the value of money remains constant over t

Nataly_w [17]

None is necessarily true.

Even though you have your money in an interest-bearing savings vehicle, its value (purchasing power) may actually decrease if the interest rate is not at least as great as the inflation rate.

In periods of inflation, the value of money decreases over time. In periods of deflation, the value of money increases over time. It tends to be difficult to regulate an economy so the value of money remains constant over time.

The present value of money is greater than the future value in inflationary times. The opposite is true in deflationary times.

_____
In the US in the middle of the last century, inflation rates were consistently 2-3% per year and savings interest rates were perhaps 4-6%. Money saved actually increased in value, and the present value of money was greater than the future value. These days, inflation is perhaps a little lower, but savings interest rates are a lot lower, so savings does not outpace inflation the way it did. The truth or falsity of all these statements depends on where and when you're talking about.

3 0

3 years ago

The probability distribution histogram shows the number of trees in yards in a certain neighborhood.

Vilka [71]

Answer:

45%

Step-by-step explanation:

Here, we want to know the probability of a randomly selected yard having 6 or more than 6 trees

To get this, we simply add up the probability of 6 yards and above

That is the probability of 6, 8 , 10 and 12 yards

This is obtainable from the histogram

We then proceed to add up from the graph

What we have is;

0.05 + 0.25 + 0.10 + 0.05

= 0.10 + 0.10 + 0.25 = 0.45

This is same as 45/100 which is otherwise 45%

4 0

3 years ago